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Aharonov Bohm oscillation in a multi-domain ferromagnetic Fe19Ni81 ring
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Physica E 18 (2003) 237 – 238 www.elsevier.com/locate/physe
Aharonov Bohm oscillation in a multi-domain ferromagnetic Fe19Ni81 ring E. Saitoh∗ , S. Kasai, H. Miyajima Department of Physics, Keio University, 3-14-1 Hiyoshi, Ko-hokuku, Yokohama 223-8522, Japan
Abstract The magnetoresistance of a ferromagnetic Fe19 Ni81 ring with 420 nm in inner diameter and 500 nm in outer diameter was measured at 4:2 K and 30 mK. When the magnetic 2eld is applied to the ring, the magnetoresistance exhibits a periodic oscillation due to the Ahoronov Bohm e5ect in both a single domain con2guration and a multi-domain con2guration. This indicates that the interference e5ect of a conduction electron in the submicron ferromagnet subsists even in the strong modulation of local magnetization. ? 2003 Elsevier Science B.V. All rights reserved. Keywords: Nanomagnets; Coherence; Aharonov Bohm e5ect
The coherent charge motion in submicron-sized ferromagnets has attracted interest due to the relevance to their transport properties at low temperatures. In submicron-sized ferromagnets, local spin modulation gives rise to the decoherence of conduction electron [1–3]. Such a decoherence is a candidate for the mechanism of the resistive changes by nucleation or annihilation of a domain wall [1], and was believed to critically suppress the quantum interference such as the Aharonov-Bohm (AB) oscillation [4] in ferromagnets. Recently, we found an AB oscillation in a ferromagnetic Fe19 Ni81 submicron ring around the magnetic 2eld of 3 T [5]. In such a magnetic 2eld range, the magnetization of the Fe19 Ni81 submicron ring is almost saturated and the domain walls disappear. This paper describes the AB oscillation in a multi-domain ferromagnetic Fe19 Ni81 ring. The result indicates that the interference e5ect in a submicron ferromagnet subsists even when the local magnetization is highly modulated. The sample investigated in the present study consists of an Fe19 Ni81 ring and wires attached to the ring edges. It was fabricated by the lift-o5 technique using electron beam lithography [5]. A scanning electron microscope image of the sample is shown in the inset in Fig. 1(a). The size of
∗
Corresponding author. E-mail address: [email protected] (E. Saitoh).
the sample is as follows: the outer diameter of the ring Do =500 nm, the inner diameter of the ring Di =420 nm, and the width of the wire w = 40 nm. The thickness of the wire and ring is 20 nm. For resistance measurement, Cu electrodes were attached to the wires. The distance between the two voltage electrodes is 2:5 m. The sample was mounted on a 3 He4 He dilution refrigerator. The temperature dependence of magnetoresistance was measured with using the conventional four probe method (25 Hz; 50 nA). The magnetic 2eld was applied at an angle of 15◦ in a perpendicular direction to the substrate (see Fig. 1(a)). The sweep rate of the magnetic 2eld was 2 Oe=s. Fig. 1(a) shows the magnetoresistance at 4:2 K. The application sequence of the magnetic 2eld is depicted by the arrows. While applying the magnetic 2eld, the resistance gradually decreases and jumps at 0:7 T, and then almost saturates around B=3 T. The 2eld dependence of the resistance is mainly caused by the anisotropic magnetoresistance e5ect (AMR) [6] typically observed in ferromagnets, indicating that the resistance jump at 0:7 T corresponds to a magnetization reversal. While decreasing the magnetic 2eld from 4 to 0 T, the resistance gradually increases without exhibiting steep change. This indicates that the remnant magnetic state is a multi-domain con2guration. Such a con2guration is also con2rmed by a magnetic force microscopy. Fig. 1(b) shows the magnetoresistance at 30 mK. Before the measurement, the external magnetic 2eld of B = 4 T was
1386-9477/03/$ - see front matter ? 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S1386-9477(02)00992-X
238
E. Saitoh et al. / Physica E 18 (2003) 237 – 238
Resistance (Ω)
1850
(a)
(b)
1845 500 nm
1840
15
1835
4.2 K Power Spectrum(10-5Ω2T)
1830 0
1
30 mK 2
3
0
1
2
3
4
H (T)
(c) 10
(d)
0
5 0
100
200
300 0
100
200
300
2π/∆B (T-1)
Fig. 1. (a,b) Magnetoresistance for a NiFe submicron-ring at 4:2 K and 30 mK (see text). The inset to (b) is a scanning electron microscope image of the sample. (c,d) Power spectra of R30 mK (B) − R4:2 K (B) for 0 ¡ B ¡ 0:2 T and 3:8 T ¡ B ¡ 4 T at 30 mK. The arrows show the peak positions.
applied, and then the resistance was measured with decreasing the magnetic 2eld. It should be noted that 2ne structures of magnetoresistance including periodic oscillations were observed at 30 mK. As reported in a previous paper [5], the periodic oscillation is due to the AB oscillation. The AB oscillation was observed in both the single domain and the multi-domain con2guration. In order to assess the oscillation in a quantitative manner, the AMR signal was removed from the magnetoresistance data at 30 mK (R30 mK (B)) by subtracting those measured with decreasing the magnetic 2eld at 4:2 K (R4:2 K (B)). Fig. 1(c) and (d) show the power spectra deduced from R30 mK (B) − R4:2 K (B) for 0 ¡ B ¡ 0:2 T and 3:8 T ¡ B ¡ 4 T, respectively. The increasing tail structure towards 2 =GB = 0 in the spectra corresponds to the UCF. The R30 mK (B) − R4:2 K (B) for 0 ¡ B ¡ 0:2 T represents quantum transport properties in a multi-domain con2guration while that for 3:8 T ¡ B ¡ 4 T represents properties in a single domain con2guration. In both the magnetic 2eld ranges, clear peak structures appear around 2 =GB=230 T−1 . The corresponding period of oscillation is GB ≈ 0:027 T, which is consistent with the expected period due to the AB oscillation, 0:020 T ¡ GB ¡ 0:029 T, given by the inner-diameter (Di ) and outer-diameter (Do ) of the
ring. This indicates that the AB oscillation in ferromagnet subsists even in the multi-domain con2guration. The amplitude of the AB oscillation observed in the multi-domain con2guration (0 ¡ B ¡ 0:2 T) is comparable to that in the single domain con2guration (3:8 T ¡ B ¡ 4 T). This indicates that the quantum decoherence due to the local spin modulation around the domain walls in Fe19 Ni81 is negligible. There are two contradicting theories for the adiabaticity relevant to the coherent electron motion in the spin modulation. One is Stern’s criterion [2] which requires !B 1= , where !B and represent the spin precession frequency due to the e5ective internal magnetic 2eld for conductive s-electrons (He5 ) and the elastic scattering time, respectively. In the present case, can be estimated to be of the order of 10−12 s from the residual resistivity. Such a small leads to unnaturally huge (10 kOe) He5 within the Stern’s criterion, indicating that the criterion cannot be responsible for the coherent charge dynamics in Fe19 Ni81 . On the other hand, Loss et al. (LSG) [3] concluded that the adiabaticity is reached at a much weaker magnetic 2eld, !B 1= (l=L)2 , where L and l represent the typical extension of the domain walls and the mean free path, respectively. In the present case, L can be estimated to be of the order of 100 nm from the magnetic force microscopy (not shown here), which allows He5 to be moderate (∼ 100 Oe). Recently, the LSG’s criterion was examined numerically; Langen et al. [7] showed that a numerical simulation of the decoherence cannot fully be accounted for by the LSG’s theory but is rather consistent with the Stern’s theory. In the present experimental study, however, the Stern’s criterion is apparently too pessimistic but less strict criterion, such as the LSG’s criterion, should be considered. This work was supported by a Grant-In-Aid from the Ministry of Education, Science, Sports and Culture of Japan. References [1] [2] [3] [4] [5]
G. Tatara, H. Fukuyama, Phys. Rev. Lett. 78 (1997) 3773. A. Stern, Phys. Rev. Lett. 68 (1992) 1022. D. Loss, et al., Phys. Rev. Lett. 48 (1993) 15 218. R.A. Webb, Phys. Rev. Lett. 54 (1985) 2696. S. Kasai, T. Niiyama, E. Saitoh, H. Miyajima, Appl. Phys. Lett., in press. [6] T.R. McGuire, et al., IEEE. Trans. Magn. MAC11 (1975) 1018. [7] S.A. van Langen, et al., Phys. Rev. B 59 (1999) 2102.
Physica E 18 (2003) 237 – 238 www.elsevier.com/locate/physe
Aharonov Bohm oscillation in a multi-domain ferromagnetic Fe19Ni81 ring E. Saitoh∗ , S. Kasai, H. Miyajima Department of Physics, Keio University, 3-14-1 Hiyoshi, Ko-hokuku, Yokohama 223-8522, Japan
Abstract The magnetoresistance of a ferromagnetic Fe19 Ni81 ring with 420 nm in inner diameter and 500 nm in outer diameter was measured at 4:2 K and 30 mK. When the magnetic 2eld is applied to the ring, the magnetoresistance exhibits a periodic oscillation due to the Ahoronov Bohm e5ect in both a single domain con2guration and a multi-domain con2guration. This indicates that the interference e5ect of a conduction electron in the submicron ferromagnet subsists even in the strong modulation of local magnetization. ? 2003 Elsevier Science B.V. All rights reserved. Keywords: Nanomagnets; Coherence; Aharonov Bohm e5ect
The coherent charge motion in submicron-sized ferromagnets has attracted interest due to the relevance to their transport properties at low temperatures. In submicron-sized ferromagnets, local spin modulation gives rise to the decoherence of conduction electron [1–3]. Such a decoherence is a candidate for the mechanism of the resistive changes by nucleation or annihilation of a domain wall [1], and was believed to critically suppress the quantum interference such as the Aharonov-Bohm (AB) oscillation [4] in ferromagnets. Recently, we found an AB oscillation in a ferromagnetic Fe19 Ni81 submicron ring around the magnetic 2eld of 3 T [5]. In such a magnetic 2eld range, the magnetization of the Fe19 Ni81 submicron ring is almost saturated and the domain walls disappear. This paper describes the AB oscillation in a multi-domain ferromagnetic Fe19 Ni81 ring. The result indicates that the interference e5ect in a submicron ferromagnet subsists even when the local magnetization is highly modulated. The sample investigated in the present study consists of an Fe19 Ni81 ring and wires attached to the ring edges. It was fabricated by the lift-o5 technique using electron beam lithography [5]. A scanning electron microscope image of the sample is shown in the inset in Fig. 1(a). The size of
∗
Corresponding author. E-mail address: [email protected] (E. Saitoh).
the sample is as follows: the outer diameter of the ring Do =500 nm, the inner diameter of the ring Di =420 nm, and the width of the wire w = 40 nm. The thickness of the wire and ring is 20 nm. For resistance measurement, Cu electrodes were attached to the wires. The distance between the two voltage electrodes is 2:5 m. The sample was mounted on a 3 He4 He dilution refrigerator. The temperature dependence of magnetoresistance was measured with using the conventional four probe method (25 Hz; 50 nA). The magnetic 2eld was applied at an angle of 15◦ in a perpendicular direction to the substrate (see Fig. 1(a)). The sweep rate of the magnetic 2eld was 2 Oe=s. Fig. 1(a) shows the magnetoresistance at 4:2 K. The application sequence of the magnetic 2eld is depicted by the arrows. While applying the magnetic 2eld, the resistance gradually decreases and jumps at 0:7 T, and then almost saturates around B=3 T. The 2eld dependence of the resistance is mainly caused by the anisotropic magnetoresistance e5ect (AMR) [6] typically observed in ferromagnets, indicating that the resistance jump at 0:7 T corresponds to a magnetization reversal. While decreasing the magnetic 2eld from 4 to 0 T, the resistance gradually increases without exhibiting steep change. This indicates that the remnant magnetic state is a multi-domain con2guration. Such a con2guration is also con2rmed by a magnetic force microscopy. Fig. 1(b) shows the magnetoresistance at 30 mK. Before the measurement, the external magnetic 2eld of B = 4 T was
1386-9477/03/$ - see front matter ? 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S1386-9477(02)00992-X
238
E. Saitoh et al. / Physica E 18 (2003) 237 – 238
Resistance (Ω)
1850
(a)
(b)
1845 500 nm
1840
15
1835
4.2 K Power Spectrum(10-5Ω2T)
1830 0
1
30 mK 2
3
0
1
2
3
4
H (T)
(c) 10
(d)
0
5 0
100
200
300 0
100
200
300
2π/∆B (T-1)
Fig. 1. (a,b) Magnetoresistance for a NiFe submicron-ring at 4:2 K and 30 mK (see text). The inset to (b) is a scanning electron microscope image of the sample. (c,d) Power spectra of R30 mK (B) − R4:2 K (B) for 0 ¡ B ¡ 0:2 T and 3:8 T ¡ B ¡ 4 T at 30 mK. The arrows show the peak positions.
applied, and then the resistance was measured with decreasing the magnetic 2eld. It should be noted that 2ne structures of magnetoresistance including periodic oscillations were observed at 30 mK. As reported in a previous paper [5], the periodic oscillation is due to the AB oscillation. The AB oscillation was observed in both the single domain and the multi-domain con2guration. In order to assess the oscillation in a quantitative manner, the AMR signal was removed from the magnetoresistance data at 30 mK (R30 mK (B)) by subtracting those measured with decreasing the magnetic 2eld at 4:2 K (R4:2 K (B)). Fig. 1(c) and (d) show the power spectra deduced from R30 mK (B) − R4:2 K (B) for 0 ¡ B ¡ 0:2 T and 3:8 T ¡ B ¡ 4 T, respectively. The increasing tail structure towards 2 =GB = 0 in the spectra corresponds to the UCF. The R30 mK (B) − R4:2 K (B) for 0 ¡ B ¡ 0:2 T represents quantum transport properties in a multi-domain con2guration while that for 3:8 T ¡ B ¡ 4 T represents properties in a single domain con2guration. In both the magnetic 2eld ranges, clear peak structures appear around 2 =GB=230 T−1 . The corresponding period of oscillation is GB ≈ 0:027 T, which is consistent with the expected period due to the AB oscillation, 0:020 T ¡ GB ¡ 0:029 T, given by the inner-diameter (Di ) and outer-diameter (Do ) of the
ring. This indicates that the AB oscillation in ferromagnet subsists even in the multi-domain con2guration. The amplitude of the AB oscillation observed in the multi-domain con2guration (0 ¡ B ¡ 0:2 T) is comparable to that in the single domain con2guration (3:8 T ¡ B ¡ 4 T). This indicates that the quantum decoherence due to the local spin modulation around the domain walls in Fe19 Ni81 is negligible. There are two contradicting theories for the adiabaticity relevant to the coherent electron motion in the spin modulation. One is Stern’s criterion [2] which requires !B 1= , where !B and represent the spin precession frequency due to the e5ective internal magnetic 2eld for conductive s-electrons (He5 ) and the elastic scattering time, respectively. In the present case, can be estimated to be of the order of 10−12 s from the residual resistivity. Such a small leads to unnaturally huge (10 kOe) He5 within the Stern’s criterion, indicating that the criterion cannot be responsible for the coherent charge dynamics in Fe19 Ni81 . On the other hand, Loss et al. (LSG) [3] concluded that the adiabaticity is reached at a much weaker magnetic 2eld, !B 1= (l=L)2 , where L and l represent the typical extension of the domain walls and the mean free path, respectively. In the present case, L can be estimated to be of the order of 100 nm from the magnetic force microscopy (not shown here), which allows He5 to be moderate (∼ 100 Oe). Recently, the LSG’s criterion was examined numerically; Langen et al. [7] showed that a numerical simulation of the decoherence cannot fully be accounted for by the LSG’s theory but is rather consistent with the Stern’s theory. In the present experimental study, however, the Stern’s criterion is apparently too pessimistic but less strict criterion, such as the LSG’s criterion, should be considered. This work was supported by a Grant-In-Aid from the Ministry of Education, Science, Sports and Culture of Japan. References [1] [2] [3] [4] [5]
G. Tatara, H. Fukuyama, Phys. Rev. Lett. 78 (1997) 3773. A. Stern, Phys. Rev. Lett. 68 (1992) 1022. D. Loss, et al., Phys. Rev. Lett. 48 (1993) 15 218. R.A. Webb, Phys. Rev. Lett. 54 (1985) 2696. S. Kasai, T. Niiyama, E. Saitoh, H. Miyajima, Appl. Phys. Lett., in press. [6] T.R. McGuire, et al., IEEE. Trans. Magn. MAC11 (1975) 1018. [7] S.A. van Langen, et al., Phys. Rev. B 59 (1999) 2102.